Cosmological constraints on dark energy parametrizations after DESI 2024: Persistent deviation from standard $\Lambda$CDM cosmology

In this work, we present a study on cosmological constraints of dark energy (DE) parametrizations after the observations of Dark Energy Spectroscopic Instruments (DESI) for Baryon Acoustic Oscillations (BAO) in 2024, suggesting potential deviations from the standard flat-$\Lambda$CDM cosmology. This study aims to put observational constraints on equation of state (EoS) parametrizations beyond the standard $\Lambda$CDM model using DESI BAO 2024 data, Cosmic Microwave Background (CMB) anisotropy observations 2018, and various Supernovae type Ia (SNIa) compilations: PantheonPlus, Union3, and Dark Energy Survey 5-year photometrically classified SNIa (DES-SN5YR). Our main goal is to validate the result of DESI collaborations \cite{DESI:2024mwx} in the context of some parametrizations beyond the Chevallier-Polarski-Linder (CPL) approximation known as Barboza-Alcaniz (BA) and Pad\'e parametrizations. These investigations allow us to examine the potential biases in the results presented by DESI collaborations with respect to CPL parametrization. By comparing our findings using BA and Pad\'e parametrizations to the CPL case, we indicate that the deviation from $w_{\Lambda} = -1.0$, observed in the CPL parametrization, is also evident in the BA and Pad\'e parametrizations.